GraphPad Statistics Guide

Interpreting results: Kaplan-Meier curves

Interpreting results: Kaplan-Meier curves

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Interpreting results: Kaplan-Meier curves

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Kaplan-Meier survival fractions

Prism calculates survival fractions using the product limit (Kaplan-Meier) method. For each X value (time), Prism shows the fraction still alive (or the fraction already dead, if you chose to begin the curve at 0.0 rather than 1.0). This table contains the numbers used to graph survival vs. time.

The calculations take into account censored observations. Subjects whose data are censored--either because they left the study, or because the study ended -- can't contribute any information beyond the time of censoring. This makes the computation of survival percentage somewhat tricky. While it seems intuitive that the curve ought to end at a survival fraction computed as the total number of subjects who died divided by the total number of subjects, this is only correct if there are no censored data. If some subjects were censored, then subjects were not all followed for the same duration, so computation of the survival fraction is not straightforward (and what the Kaplan-Meier method is for).

If the time of death of some subjects is identical to the time of censoring for others, Prism does the computations assuming the deaths come first.

Confidence intervals of survival percentages

Prism reports the uncertainty of the fractional survival as a standard error or 95% confidence intervals. Standard errors are calculated by the method of Greenwood.

You can choose between two methods of computing the 95% confidence intervals:

Asymmetrical method (recommended). It is computed using the log-log transform method, which has also been called the exponential Greenwood formula.  It is explained on page 42 and page 43 of Machin (reference below). You will get the same results from the survfit R function by setting error to Greenwood and conf.type to log-log. These intervals apply to each time point. The idea is that at each time point, there is a 95% chance that the interval includes the true population survival. We call the method asymmetrical because the distance that the interval extends above the survival time does not usually equal the distance it extends below. These are called pointwise confidence limits. It is also possible (but not by Prism) to compute confidence bands that have a 95% chance of containing the entire population survival curve. These confidence bands are wider than pointwise confidence limits.

Symmetrical method. These intervals are computed as 1.96 times the standard error in each direction. In some cases the confidence interval calculated this way would start below 0.0 or end above 1.0 (or 100%). In these cases, the error bars are clipped to avoid impossible values. We provide this method only for compatibility with older versions of Prism, and don't recommend it.

Number of subjects at risk at various times

One of the pages (or 'views') in the survival analysis page is "# of subjects at risk". Since the number at risk applies to a range of days, and not to a single day, the table is a bit ambiguous.

Here are the top six rows of that table for the sample data (comparing two groups) that you can choose from Prism's Welcome dialog.

Days

Standard

Experimental

0

16

14

90

16


142

15


150

14


369

13


272


14

The experiment starts with 16 subjects receiving standard therapy and 14 receiving experimental therapy. On day 90, one of the patients receiving standard therapy died. So the value next to 90 tells you that there were 16 subjects alive up until day 90, and 15 at risk between day 90 and 142. At day 142, the next patient dies, also on standard therapy. So between days 142 and 150 (the next death), 14 subjects are at risk in the standard group.

Prism does not graph this table automatically. If you want to create a graph of number of subjects at risk over time, follow these steps:

1.Go to the results subpage of number of subjects at risk.

2.Click New, and then Graph of existing data.

3.Choose the XY tab and a graph with no error bars.

4.Change the Y-axis title to “Number of subjects at risk” and the X-axis title to “Days”.

Reference

David Machin, Yin Bun Cheung, Mahesh Parmar, Survival Analysis: A Practical Approach, 2nd edition, IBSN:0470870400.